Week 1: Perceptrons, Backpropagation & Learning Dynamics
Understand the building blocks of neural networks from first principles: perceptrons, backpropagation mathematics, activation functions, and optimization dynamics.
- Derive the backpropagation algorithm from chain rule calculus
- Implement a 2-layer network in pure NumPy
- Understand the role of different activation functions
- Debug common neural network training problems
This first lecture establishes the foundational framework for Neural Networks Fundamentals. By the end of this session, you will have the conceptual grounding and practical starting point needed for the rest of the course.
Key Concepts
The lecture introduces the four main pillars of this course: Perceptron Learning Algorithm, MLP: Forward & Backward Pass, Activation Functions: ReLU, Sigmoid, Tanh, Optimizer Dynamics: SGD, Momentum, Adam. Each will be explored in depth over the 14-week curriculum, with hands-on projects reinforcing theory at every stage.
This Week's Focus
Focus on mastering: Perceptron Learning Algorithm and MLP: Forward & Backward Pass. These are the prerequisites for everything in Week 2. The concepts build on each other — do not skip the practice exercises.
AI203 Project 1: Neural Network from Pure NumPy
Build a full multi-layer neural network using only NumPy: forward pass, backpropagation, mini-batch SGD. Train on MNIST and achieve >95% accuracy. No PyTorch or TensorFlow allowed.
- NumPy neural network (2+ layers, configurable)
- Backpropagation implementation with gradient checking
- Training curves: loss and accuracy vs epoch
- Architecture ablation study (width, depth, activation)
These represent the style and difficulty of questions you'll see on the midterm and final. Start thinking about them now.
Derive ∂L/∂W for a fully connected layer using the chain rule. Show all intermediate steps.
Why does the sigmoid activation function cause vanishing gradients in deep networks?
Compare SGD, SGD+momentum, and Adam. What problem does each optimizer address?